Alexandrov空间的可定向性和基本类及其应用
Orientability and fundamental classes of Alexandrov spaces with applications
摘要：
在本文中，我们考虑了几个有效的概念的Alexandov空间的定向性，并证明了所有这些条件是等价的。进一步，我们给出了可定向性的拓扑和几何应用。特别地，证明了一个Poincaré型对偶定理。作为对偶定理的一个推论，我们还证明了，如果一个封闭的亚历山德罗夫空间承认一个正曲率界在一个综合的意义上，那么它的余维一个同调消失。进一步，我们得到了可定向闭Alexandrov空间的一个填充半径不等式.
英文摘要：
In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geometric applications of the orientability. In particular, a Poincaré-type duality theorem is proved. As a corollary to the duality theorem, we also prove that if a closed Alexandrov space admits a positive curvature bound in a synthetic sense, then its codimension one homology vanishes. Further, we obtain a filling radius inequality for closed orientable Alexandrov spaces.
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